We develop BayesianMarkov chain Monte Carlo methods for inferences of continuous-time models with stochastic volatility and infinite-activity Lévy jumps using discretely sampled data. Simulation studies show that (I) our methods provide accurate joint identification of di.usion, stochastic volatility, and Lévy jumps, and (ii) a.ne jump-di.usion models fail to adequately approximate the behavior of infinite-activity jumps. In particular, the affine jump-diffusion models fail to capture the “infinitely many”small Lévy jumps which are too big for Brownian motion to model and too small for compound Poisson process to capture. Empirical studies show that infinite-activity Lévy jumps are essential for modeling the S&P 500 index returns.
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机译：我们开发Bayesianmarkov Chain Monte Carlo Monte Carlo方法，用于随机波动和无限活动跳跃的连续时间模型，使用离散采样数据跳跃。仿真研究表明，我们的方法提供了准确的联合识别DI.USCE，随机波动性和Lévy跳跃，（ii）A.Ne Jump-DI.USCE模型未能充分接近无限活动跳跃的行为。特别是，仿射跳跃扩散模型未能捕获“无限许多”的小Lévy跳跃，这对于布朗运动来说太大，对于模型而言，对于复方泊松过程来捕获，这太小了。实证研究表明，无限活动Lévy跳跃对于建模标准普尔500指数回报是必不可少的。
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